I've Got It
The most basic principle for a teacher is not to mislead students.
Shen Qi performed reasonably well during the transition period.
The most important event recently is, of course, the International Congress of Mathematicians in late October.
With just over a month to go, Shen Qi is preparing for the competition in a tense but organized manner.
All the task data that Jonas, Mary, and Ou Ye were responsible for were compiled and handed over to Shen Qi.
Shen Qi checked and verified each item one by one, and then entered the final stage of compiling the manuscript.
"The first path that Jonas was responsible for was based on the twin matching method. By analyzing the function log(s), he obtained that ∏L(s,Χ) is analytically equal to zero at the point s=1... It was so-so. Jonas is a bit of a nutcase; his performance is inconsistent. Overall, I would give him a 60 out of 100 for the first path he was responsible for."
Jonas's derivation results were unsatisfactory, and Shen Qi needed to complete the remaining work on the first path of the RT Third Expression himself.
"Mary was in charge of the second path, based on the fundamental theorem of prime numbers. She derived a corollary to support the RT Third Expression. She pointed out that when c is a positive constant dependent on A, and A > 1, we have π(x; q, l) = Lix/φ(q) + O(xe^-clogx)... Mary did a great job, I give her 90 points."
Mary did Shen Qi a great favor, as he could directly use the important deductions she obtained.
"The third path that Little Yezi was in charge of was the most difficult, requiring the finding of the crucial support for the RT Third Expression through the zero-point equation... Hey, she found it!"
Ou Ye's information was sent to Princeton three days ago. After spending the night at Shen Qi's apartment, Ou Ye has returned to Columbia University.
Shen Qi studied Ou Ye's information carefully today. He was very excited and gave Ou Ye a score of 99.
Shen Qi made a phone call to Ou Ye, "Little Yezi, when T is not the ordinate of the zero point of L(s, X), did you complete the zero-point equation by yourself? Did Professor Gong contribute anything to it?"
Ou Ye: "Professor Gong gave me some guidance."
"So, you mean you completed most of the tasks you were in charge of yourself?" Shen Qi asked.
Ou Ye: "More or less."
"How did you suddenly become so amazing? This zero-point equation is very difficult. Based on my initial assessment, you did a very good job, almost perfectly." Shen Qi was both surprised and delighted.
Ou Ye: "You'll become more proficient once you solve more equations."
Shen Qi laughed heartily, "Right, right, that's right! Solving equations requires continuous practice. I know you've been working very hard on solving equations lately, and I acknowledge that. Three days ago, you were at my apartment, and you actually..."
"You're so annoying!" Ou Ye said playfully on the other end of the phone, then instructed, "I won't be visiting you lately, and don't come looking for me either. Focus on preparing for the Fields Medal."
"Okay, I definitely won't let you down, and I won't let the team down!" Shen Qi said firmly, ending the call with Ou Ye.
The collaborative editing work took Shen Qi a week.
Shen Qi didn't need to put in much effort to compile the information on Ou Ye and Mary; a little sorting was enough.
Shen Qi's main task was to refine and supplement Jonas's information.
Every project leader hopes that their team members are all highly skilled and capable, and that these individuals are always at their peak academic level, so that the project leader only needs to do the copy-and-paste work.
This is the ideal setting, but reality often falls short of this ideal.
Therefore, in addition to having a strategic vision, the project leader also needs to have strong tactical skills, be able to identify and fill gaps at any time, and personally improve the project paper.
Twenty days before the International Congress of Mathematicians, Shen Qi published a paper on arVix entitled "Research on the RT Third Expression".
This paper, totaling 66 pages, is an update and supplement to the report that Shen Qi presented in Italy.
In order to prove the Riemann Hypothesis, Shen Qi derived two core expressions. That paper made Shen Qi famous overnight, and he was promoted to the ranks of the world's top mathematicians.
The papers on the first two expressions of the Riemann Hypothesis are only 30 pages long, while the paper on the RT Third Expression is 66 pages long, which fully illustrates that the derivation process of the third expression is more complex.
During this special period, any slight movement by the top candidates for the Fields Medal will attract deep attention from the international Mathematics Community and the media.
Shen Qi published his latest research progress on the RT Third Expression 20 days ahead of schedule, in order to allow the international Mathematics Community some time to study his latest results.
"Shen Qi has published his latest research findings on the RT Third Expression. In this 66-page paper, Shen Qi and his team obtained two corollaries and a core equation of the RT Third Expression through three paths. This is a very important breakthrough. Combined with the first two expressions proven by the Riemann Hypothesis, Shen Qi has almost secured a Fields Medal." - Comments and predictions from the American Mathematics Community.
"First, we must acknowledge Shen Qi's contributions, but the problem is that the RT Third Expression has not been fully proven. The fourth path that Shen Qi mentioned at the Ramanujan Prize presentation remains unproven." - Comment from the European Mathematics Community.
The fourth proof path, which is the most important aspect of the RT Third Expression, is the responsibility of Shen Qi himself.
Recently, Shen Qi has been staying indoors, and Professor Lyndon Strauss has been taking over all the undergraduate number theory courses.
He drank all the alcohol he could, and burned all the draft papers he could, Shen Qi didn't write down a single symbol related to the fourth path.
"Professor Wiles's mysterious ritual is completely useless."
Shen Qi burned only draft papers; he couldn't bear to burn the completed formal papers.
To solve mathematical problems, one should start with mathematics itself.
What kind of alcohol do you drink? What kind of academic paper do you burn?
Feudal and superstitious ideas have caused immense harm to people!
There is one week left until the opening of the International Congress of Mathematicians.
Shen Qi no longer drinks or burns papers; he returns to mathematics itself, number theory itself, and Analytic Number Theory itself.
Mathematicians usually divide mathematics into pure mathematics and applied mathematics. Number theory undoubtedly belongs to pure mathematics, and Analytic Number Theory is the purest of all.
Disciplines that are too theoretical are destined to be toys for a very few people; they are lonely and isolated at the top.
Analytic Number Theory, a very demanding analytical discipline, is not popular in China. However, some of the most famous mathematicians in modern China are closely associated with Analytic Number Theory.
In China, there are generally two schools of thought on Analytic Number Theory: one is the Chinese Academy of Sciences school, with Hua Luogeng as its core, and the other is the Yanjing School, with Min Sihe as its guiding principle.
Another outstanding representative of the Chinese Academy of Sciences school is Mr. Chen Jingrun, Goldbach Conjecture is a famous problem in Analytic Number Theory.
Academician Lin at Yenching Big Mathematics Department of Mathematical Sciences specializing in number theory, was a student of Min Sihe. He had exchanges with Shen Qi during the period when Shen Qi returned to China at the end of June.
"I derived this formula, where s is a variable, and a complex variable. We can clearly see that at the zero point, this formula is obtained entirely through the transformation of the entire function ξ(s), and it is still an entire function in form..."
Shen Qi recalled Academician Lin's views at the time.
"Therefore, we can imagine that during the traversal of the complex plane, s happens to be exactly at a non-obvious zero point, that is, it coincides with that non-obvious zero point. It is not difficult to deduce that the value of this expression is 0. The RT Third Expression is thus proved..."
Just then, dark clouds suddenly filled the sky over Princeton.
Rumble!
A thunderclap resounded.
A torrential downpour began.
Shen Qi was suddenly struck by a brilliant idea, as if his brain had been struck by lightning.
"Academician Lin's point is valid, but it needs further refinement before the RT Third Expression can be finally proven."
"Haha, hahaha, I've already figured out how to improve it..."